An iron tyre is to be fitted onto a wooden wheel 1.0 m in diameter. The diameter of the tyre is 6 mm smaller than that of the wheel. The tyre should be heated so that its temperature increases by a minimum of (coefficient of volume expansion of iron is ).
Answers
Answer:
500°c
Step-by-step explanation:
Most materials are tend to undergo thermal expansion which shows expansion when heated and contraction when cooled.
To calculate the volume change during expansion or contraction the formula δV = bVoδT, the last term does means change in temperature while δV means change in volume wheras Vo is the original volume.
As tyre is 6mm short of what it's meant to be to wooden wheel of 1m
Initial diameter of tyre 1000-6=994mm
Hence radius = 497mm
And elongation in radius will be 3mm
Increasing temp δT will lead to the tire fitting in the circumference
Dl=l*a*δT
Here a will be ¥/3 ¥ denotes gamma
Also δT will lead to change in d0 where 0 denotes theta
Thus
Dl= L*¥/3*∆0
2π∆R=2πR*¥/3*∆0
∆0=3*∆R/¥R
Putting the values as
∆R=3
¥=3.6*10^-5 (coefficient of volume expansion of iron)
R=497
∆0= 500°c